Dimensional Analysis Calculator
Chain up to three conversion factors to convert a quantity step by step — the factor-label method that makes units cancel cleanly.
How it works
Result = start × (n₁ ÷ d₁) × (n₂ ÷ d₂) × (n₃ ÷ d₃)
Dimensional analysis, or the factor-label method, converts a quantity by multiplying it through a chain of conversion factors, each written so an unwanted unit cancels top-against-bottom. Because every factor equals 1, the numeric value changes but the physical quantity does not. Set any factor you do not need to 1/1 so it passes through untouched.
Worked example
Convert 2 hours to seconds. Multiply by 60 min / 1 hr, then 60 s / 1 min: 2 × 60/1 × 60/1 = 7,200 seconds. The “hours” and “minutes” labels cancel down the chain, leaving seconds.
Frequently asked questions
How do I know which way up to write each factor?
Write each factor so the unit you want to get rid of is on the bottom, cancelling the unit above it from the previous step. The unit you are heading toward should end up on top of the last factor.
What if I only need one or two factors?
Leave the unused factors as 1 / 1. Multiplying by 1/1 does nothing, so a single- or double-step conversion works without touching the extra rows.
Why use this instead of just multiplying and dividing?
Tracking the units as you go is a built-in error check: if the labels do not cancel to the unit you expect, you have set a factor upside down. It catches mistakes that a bare calculation hides.
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This calculator is for educational purposes. Double-check important results before acting on them.